The present invention relates to the general and optimal decoding and characterization of any non-stationary signal that is given say, as a function of time. The method is general in nature because it applies to all non-stationary as well as stationary signals irrespective of origin. By virtue of the algebraic structure underlying the circuit connections, the method is also optimal in the informaion theoretic sense of Shannon. One of the major reasons of its optimality, even on non-stationary signals, is readily seen by contrasting the invention to known methods of signal characterization.
Practically all known methods for characterization of time dependent functions, for example the methods of Fourier transformation, Laguerre filtering, Wiener canonical expansion, Hadamard matrices, Walsh transforms, and so forth, are limited to stationary signals because they use tine windows as basic inputs and assume or impose stationarity within them, or transform immediately into a non-time domain or, finally, they enforce time partitions such that any continuous monitoring of non-stationary phenomena is both disrupted and lost for purposes of further decoding. The mathematical equivalence between orthogonalization and stationarity has been pointed out with emphasis by A. Sommerfeld in his "Lectures on Theoretical Physics, Volume VI: Partial Differential Equations in Physics" New York 1949 (Academic Press Inc.) The limitations of digital computers which are both sequential rather than parallel devices and sampling rather than continuous devices are also well known.
No present day devices exist for processing non-stationary signals which do not make stationarity assumptions in their attempts toward decoding, nor can present day devices approach the theoretical limit in bandwidth compression for purposes of encoding. The processing of stationary signals has been accomplished by the present day technology in the form of fast Fourier, fast Hadamard, or fast Walsh transform processors, etc. However, analysis shows that much potential information is lost when a non-stationary signal is processed through such devices which make stationarity assumptions. Even a delay line tapped at appropriate points to facilitate a fast Fourier transform (FFT) whose multitude of time windows is adaptive to the duration of individual periods of harmonics is limited to less than complete decoding by the fact that the FFT outputs all have the same physical dimension and, thus, do not exhaust all informaion theoretic classes into which non-stationary information can be encoded.
Since most signals in the real world are non-stationary, their individuality and recognizability are manifested in their non-stationary features. Some specific examples of non-stationary signals are acoustic signals generated from starting an engine or dropping an object to the floor wth the stated objective of identifying the type of engine or object. On the other hand, the sustained sound of a smoothly running engine is an example of an approximately stationary signal. All present day procesors make the initial assumption that signals being processed are stationary over several periods of harmonics and/or trust that the extractable stationary features of the same physical quality are adequate to characterize and recognize non-stationary signals. Generally, this is not the case.